Question: Rewrite as a simplified fraction. ${1.6\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 163.3333...\\ 10x &= 16.3333...\end{align*}}$ Subtracting the two equations, we have: ${90x = 147}$ ${x = \dfrac{147}{90}} $ ${x = \dfrac{49}{30}} \text{or} {1 \dfrac{19}{30}}$